无陀螺捷联惯导系统初始对准技术研究
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摘要
无陀螺捷联惯导系统(GFSINS)作为一种自主式导航系统,具有寿命长、成本低、能耗低、反应速度快等特点。由于传统的捷联惯导系统不太适合应用于大过载、大角速度的场合,而无陀螺捷联惯导系统在具有大加速度、大角速度的情况下,仍能正常工作。所以,近年来,无陀螺捷联惯导系统得到广泛研究,取得了许多研究成果,但仍然离工程化、实用化有一定差距。鉴于此,论文以无陀螺捷联惯导系统作为研究对象,分别从加速度计配置、角速度解算、静基座初始对准、动基座初始对准几个方面问题进行了研究讨论。
首先,根据构成无陀螺捷联惯导系统的加速度计配置的可行性条件,用扩展配置矩阵来分析在有加速度计失效的情况下,判断导航信息是否可完全解算。分析并给出无陀螺捷联惯导系统独立导航的加速度计配置条件。鉴于实用化的考虑,针对自主式对准的无陀螺捷联惯导系统所需要求,采用一种十二加速度计配置的无陀螺捷联惯导系统,该配置方案可在有加速度计失效的情况下,采用不同的加速度计配置方案保证系统的正常工作。
其次,为了提高系统初始对准精度,对角速度解算方法进行研究。分析积分法和开平方法角速度解算方法的优缺点；详细分析对数算法解算角速度出现问题的原因,并改进对数算法,对积分法、开平方法和改进对数算法解算角速度进行仿真验证。为了消除加速度计随机噪声对解算结果的影响,选择适合的滤波器来估计角速度。
接着,研究无陀螺捷联惯导系统静基座初始对准问题。研究初始时刻角速度符号的判断方法,并利用开平方法解算角速度的绝对值来确定初始时刻角速度,进而完成粗对准。在失准角为小角度情况下,建立无陀螺捷联惯导系统的误差方程,利用Kalman滤波进行误差估计。由于误差协方差需要在Kalman滤波运算后才能得到各状态的估计效果,而基于分段定常系统(Piece Wise Constant System,简称PWCS)的奇异值可观测度分析方法不需要事先进行Kalman滤波运算,就能得到系统各状态变量的可观测度,将PWCS的奇异值可观测度分析方法应用于GFSINS的误差方程中,为系统方案设计节省了时间。根据角速度常值解算误差,研究角速度常值解算误差的确定方法,利用PWCS的奇异值可观测度分析方法来分析角速度常值解算误差能否利用Kalman滤波器估计出来。在初始方位失准角为大角度情况下,推导非线性对准误差方程,研究EKF、UKF两种非线性滤波方法,对UKF中状态方差阵Pk可能出现负定的情况,利用奇异值分解方法的UT变化来计算Sigma点,求解状态方差阵,对比EKF、SUKF两种非线性滤波方法。
最后,研究无陀螺捷联惯导系统动基座初始对准问题。分析杆臂效应、载体的震动和挠曲运动对传递对准的影响,推导传递对准模型的误差方程,其中状态方程是惯导系统的误差方程,而量测方程与传递对准的匹配方法相关,匹配方法不同,则量测方程的形式也就不同。本文以无陀螺捷联惯导系统作为子惯导系统,推导速度匹配传递对准的误差方程；推导姿态角匹配和姿态矩阵匹配两种基于姿态信息的匹配算法,对两种匹配方法进行比较；对姿态矩阵匹配传递对准方法进行改进。
Gyroscope-free strapdown inertial navigation system (GFSINS) as an autonomous navigation system has the characteristics with a long life, low cost, low energy consumption, fast response. Traditional strapdown inertial navigation system does not apply in fields of large overload, large angular velocity. GFSINS fixes accelerometer on the carrier, uses the accelerometer output signal to solve linear acceleration and angular velocity vector. This method is especially suitable for difficult situations used in routine application SINS as large acceleration and large angular velocity. This paper discusses aspects of GFSINS, which includes accelerometer configuration, angular velocity calculation, initial alignment approach on stationary base, initial alignment approach on dynamic base.
Firstly, the feasibility of GFSINS configuration is given:configuration matrix J is full rank. If accelerometer is failed, when isolates failure of the accelerometer, use the remaining accelerometer to constitute GFSINS, and then proposes using the extended configuration matrix to analyze this case, judge navigation information can be completely calculated or not. This paper analyzes accelerometer configuration conditions rely on outside information form, independent GFSINS. Considering engineering realization, a twelve-accelerometer configuration is used in GFSINS, when one accelerometer is failed, it can be ensure to work properly with the different presentation for the system.
Secondly, angular velocity calculation methods are studied for promoting navigation precision. The advantages and disadvantages are analyzed to methods of integral algorithm, extraction algorithm and logarithmic algorithm for solving angular velocity, and simulation verification. In order to eliminate the influence of random noises of accelerometer, a kind of adaptive filter is designed. Simulation is complete under the different magnitude of noise, variety of noise and initial estimated valve of state variable, and results show adaptive filter has better precision than Kalman filter.
Then, initial alignment approach on stationary base of GFSINS is studied. To calculate the initial angular velocity of GFSINS, a method is present to determine the symbol of initial angular velocity and uses absolute value of extraction algorithm for angular velocity calculating to determine the initial angular velocity, and then completes the initial coarse alignment. In the case of small misalignment angle, the error equations of the GFSINS are established, Kalman filter is used for error estimates. Since the error covariance in the Kalman filtering method needs to be operational before the estimated effect of each state, and based on Piece Wise Constant System,(referred to PWCS) singular value analysis method does not require a substantial measure prior Kalman filter operation, system state variables can be considerable measure, for the system design time savings. Presents a constant angular velocity calculating method for determining the error, this method can analyze the error calculating constant angular velocity can be estimated using Kalman filter. When the initial azimuth misalignment angle is big, the nonlinear alignment error equations are derived, and the nonlinear filtering methods of EKF and UKF are studied. Because of the possible problem of the state covariance matrix in UKF, The singular value decomposition method of UT transformation is used to calculate Sigma point, and then solves the state covariance matrix. Compared with two nonlinear filtering methods, the results show that the performance of improved UKF algorithm is superior to EKF.
Finally, initial alignment approach on dynamic base of GFSINS is studied. The impacts on transfer alignment are lever arm effect and flexural movement. Error equations of transfer alignment model are derived, in which the error state equations are the equation of the system, while the measurement equations of transfer alignment model are related to the methods of matching transfer alignment. The measurement equation of the form is different from matching methods. This article discusses several transfer alignment methods, analyzes the advantages and disadvantages of several methods of matching transfer alignment through simulation. Attitude matrix matching method for the transfer alignment is improved, studies the practical of improved attitude matrix matching method, and receives conclusions.
首先,根据构成无陀螺捷联惯导系统的加速度计配置的可行性条件,用扩展配置矩阵来分析在有加速度计失效的情况下,判断导航信息是否可完全解算。分析并给出无陀螺捷联惯导系统独立导航的加速度计配置条件。鉴于实用化的考虑,针对自主式对准的无陀螺捷联惯导系统所需要求,采用一种十二加速度计配置的无陀螺捷联惯导系统,该配置方案可在有加速度计失效的情况下,采用不同的加速度计配置方案保证系统的正常工作。
其次,为了提高系统初始对准精度,对角速度解算方法进行研究。分析积分法和开平方法角速度解算方法的优缺点；详细分析对数算法解算角速度出现问题的原因,并改进对数算法,对积分法、开平方法和改进对数算法解算角速度进行仿真验证。为了消除加速度计随机噪声对解算结果的影响,选择适合的滤波器来估计角速度。
接着,研究无陀螺捷联惯导系统静基座初始对准问题。研究初始时刻角速度符号的判断方法,并利用开平方法解算角速度的绝对值来确定初始时刻角速度,进而完成粗对准。在失准角为小角度情况下,建立无陀螺捷联惯导系统的误差方程,利用Kalman滤波进行误差估计。由于误差协方差需要在Kalman滤波运算后才能得到各状态的估计效果,而基于分段定常系统(Piece Wise Constant System,简称PWCS)的奇异值可观测度分析方法不需要事先进行Kalman滤波运算,就能得到系统各状态变量的可观测度,将PWCS的奇异值可观测度分析方法应用于GFSINS的误差方程中,为系统方案设计节省了时间。根据角速度常值解算误差,研究角速度常值解算误差的确定方法,利用PWCS的奇异值可观测度分析方法来分析角速度常值解算误差能否利用Kalman滤波器估计出来。在初始方位失准角为大角度情况下,推导非线性对准误差方程,研究EKF、UKF两种非线性滤波方法,对UKF中状态方差阵Pk可能出现负定的情况,利用奇异值分解方法的UT变化来计算Sigma点,求解状态方差阵,对比EKF、SUKF两种非线性滤波方法。
最后,研究无陀螺捷联惯导系统动基座初始对准问题。分析杆臂效应、载体的震动和挠曲运动对传递对准的影响,推导传递对准模型的误差方程,其中状态方程是惯导系统的误差方程,而量测方程与传递对准的匹配方法相关,匹配方法不同,则量测方程的形式也就不同。本文以无陀螺捷联惯导系统作为子惯导系统,推导速度匹配传递对准的误差方程；推导姿态角匹配和姿态矩阵匹配两种基于姿态信息的匹配算法,对两种匹配方法进行比较；对姿态矩阵匹配传递对准方法进行改进。
Gyroscope-free strapdown inertial navigation system (GFSINS) as an autonomous navigation system has the characteristics with a long life, low cost, low energy consumption, fast response. Traditional strapdown inertial navigation system does not apply in fields of large overload, large angular velocity. GFSINS fixes accelerometer on the carrier, uses the accelerometer output signal to solve linear acceleration and angular velocity vector. This method is especially suitable for difficult situations used in routine application SINS as large acceleration and large angular velocity. This paper discusses aspects of GFSINS, which includes accelerometer configuration, angular velocity calculation, initial alignment approach on stationary base, initial alignment approach on dynamic base.
Firstly, the feasibility of GFSINS configuration is given:configuration matrix J is full rank. If accelerometer is failed, when isolates failure of the accelerometer, use the remaining accelerometer to constitute GFSINS, and then proposes using the extended configuration matrix to analyze this case, judge navigation information can be completely calculated or not. This paper analyzes accelerometer configuration conditions rely on outside information form, independent GFSINS. Considering engineering realization, a twelve-accelerometer configuration is used in GFSINS, when one accelerometer is failed, it can be ensure to work properly with the different presentation for the system.
Secondly, angular velocity calculation methods are studied for promoting navigation precision. The advantages and disadvantages are analyzed to methods of integral algorithm, extraction algorithm and logarithmic algorithm for solving angular velocity, and simulation verification. In order to eliminate the influence of random noises of accelerometer, a kind of adaptive filter is designed. Simulation is complete under the different magnitude of noise, variety of noise and initial estimated valve of state variable, and results show adaptive filter has better precision than Kalman filter.
Then, initial alignment approach on stationary base of GFSINS is studied. To calculate the initial angular velocity of GFSINS, a method is present to determine the symbol of initial angular velocity and uses absolute value of extraction algorithm for angular velocity calculating to determine the initial angular velocity, and then completes the initial coarse alignment. In the case of small misalignment angle, the error equations of the GFSINS are established, Kalman filter is used for error estimates. Since the error covariance in the Kalman filtering method needs to be operational before the estimated effect of each state, and based on Piece Wise Constant System,(referred to PWCS) singular value analysis method does not require a substantial measure prior Kalman filter operation, system state variables can be considerable measure, for the system design time savings. Presents a constant angular velocity calculating method for determining the error, this method can analyze the error calculating constant angular velocity can be estimated using Kalman filter. When the initial azimuth misalignment angle is big, the nonlinear alignment error equations are derived, and the nonlinear filtering methods of EKF and UKF are studied. Because of the possible problem of the state covariance matrix in UKF, The singular value decomposition method of UT transformation is used to calculate Sigma point, and then solves the state covariance matrix. Compared with two nonlinear filtering methods, the results show that the performance of improved UKF algorithm is superior to EKF.
Finally, initial alignment approach on dynamic base of GFSINS is studied. The impacts on transfer alignment are lever arm effect and flexural movement. Error equations of transfer alignment model are derived, in which the error state equations are the equation of the system, while the measurement equations of transfer alignment model are related to the methods of matching transfer alignment. The measurement equation of the form is different from matching methods. This article discusses several transfer alignment methods, analyzes the advantages and disadvantages of several methods of matching transfer alignment through simulation. Attitude matrix matching method for the transfer alignment is improved, studies the practical of improved attitude matrix matching method, and receives conclusions.
引文
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